To find the amount Rob will have in 5 years with compound interest, we can use the formula:
A = P (1 + r/n)^(nt)
where:
A = the future value of the investment
P = the principal amount invested
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
P = $7,869 (the principal amount)
r = 13% or 0.13 (the annual interest rate)
n = 1 (the interest is compounded annually)
t = 5 (the number of years)
Substituting these values into the formula, we get:
A = $7,869 (1 + 0.13/1)^(1*5)
A = $7,869 (1.13)^5
A = $14,964.92
Therefore, to the nearest cent, Rob will have $14,964.92 in 5 years.